Rotational/Linear motion & friction

In summary, the problem involves a 2.4 kg block attached to a solid drum of mass 0.80 kg and radius 5.0 cm on a 30° slope. The block accelerates down the slope at 1.2 m/s2, and the goal is to find the coefficient of friction between the block and slope. The solution involves using the work-energy theorem and the equations F = ma and torque = Iα.
  • #1
Nick_L
7
0

Homework Statement



A 2.4 kg block rests on a 30° slope and is attached by a string of negligible mass to a solid drum of mass 0.80 kg and radius 5.0 cm, as shown in Fig. 10.29. When released, the block accelerates down the slope at 1.2 m/s2. What is the coefficient of friction between block and slope?

Homework Equations



Ff=mu*N

a=alpha*r

Torque=I*alpha


The Attempt at a Solution



Ok the first thing I did was draw a free-body diagram of the block and the drum. I have Fnet=mg-Tension-mu*Fnormal then and set Tension=torque and got T=1/2*Mdrum*a and put that back into the original equation and solved for mu, but I didn't get the right answer. Is this even the right way to do this?
 
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  • #2
Welcome to PF!

Hi Nick_L! Welcome to PF! :smile:
Nick_L said:
A 2.4 kg block rests on a 30° slope and is attached by a string of negligible mass to a solid drum of mass 0.80 kg and radius 5.0 cm, as shown in Fig. 10.29. When released, the block accelerates down the slope at 1.2 m/s2. What is the coefficient of friction between block and slope?

I don't get it … what's the drum doing? :confused:

is it rotating on a fixed horizontal axis, with the string unwinding, or on a fixed vertical axis, or is it sliding down the hill on its base?
 
  • #3
Here is the picture associated with the problem

12-47.gif
 
  • #4
ok … rotating on a fixed horizontal axis, presumably with a frictionless axle, and with the string unwinding …

so use the work-energy theorem … work done = energy lost, using the mass of the object and the moment of inertia of the drum :wink:
 
  • #5
Ok so I would have Ffriction*dcos(30)=1/2*massbox*v2+1/2I*omega2? If that's right it makes sense, but how would I find displacement or velocity when I only have the acceleration?
 
  • #6
Nick_L said:
Ok so I would have Ffriction*dcos(30)=1/2*massbox*v2+1/2I*omega2? If that's right it makes sense, but how would I find displacement or velocity when I only have the acceleration?

(you left out gravity)

sorry, I missed the acceleration :redface: …

in that case, just use F = ma and torque = Iα and slug it out! :smile:
 
  • #7
Alright, thanks for the help :biggrin:
 

1. What is the difference between rotational and linear motion?

Rotational motion refers to the movement of an object around a fixed axis, while linear motion is the movement of an object in a straight line. In rotational motion, an object's position and direction of movement are described by its angle of rotation, while in linear motion, the position and direction are described by its displacement and velocity.

2. How does friction affect rotational and linear motion?

Friction is a force that resists the motion of an object. In rotational motion, friction can cause an object to slow down or stop its rotation, while in linear motion, it can slow down or stop the object's movement. Friction also causes objects to heat up, as the energy of motion is converted into heat.

3. What factors affect the amount of friction in a system?

The amount of friction in a system is affected by several factors, including the type of surfaces in contact, the force pressing the two surfaces together, and the roughness of the surfaces. The type of lubrication present can also affect the amount of friction in a system.

4. How can friction be reduced in a system?

There are several ways to reduce friction in a system. One way is to use a lubricant, such as oil or grease, to create a barrier between two surfaces. Another way is to use smooth materials or add a smoother surface, such as a ball bearing, to reduce the amount of contact between surfaces. Additionally, reducing the force pressing the two surfaces together can also decrease friction.

5. What is the importance of understanding rotational and linear motion in engineering and everyday life?

Understanding rotational and linear motion is crucial in engineering as it allows for the design and analysis of various systems and machines. It also helps in predicting and preventing potential failures due to friction. In everyday life, understanding these types of motion can help us perform tasks more efficiently, such as riding a bike or using simple machines like levers and pulleys.

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